The Belousov-Zhabotinsky reaction is an amazing looking chemical reaction that can be simulated with some pretty simple maths. I've written about it several times and recreated it in several technologies. As part of my "running before I can walk" dive into Houdini, I've implemented the simulation in VEX. First things first, a few important acknowledgements. This tutorial from Entagma on creating Mandelbrot sets in Houdini got me up and running with Point Wrangle nodes and cgwiki which is an awesome repository of technical Houdini wizardry that I've been jumping to all day. The project is pretty simple: I have a grid geometry to which I add a Solver geometry node. The solver allows for iteration: it contains a "previous frame" Dop Import node which allows me to use the values from the previous frame inside a VEX expression. To the previous frame node, I add a Point Wrangle containing the Belousov maths. This requires values for three chemicals and for those, I use to red, green and blue values of each point. Part of the equation is to get the average of the neighboring cells and to do this, I use pcopen() and pcfilter()(thanks again to cgwiki!). The final VEX is:
It's been a fairly busy few months at my "proper" job, so my recreational Houdini tinkering has taken a bit of a back seat. However, when I saw my Swarm Chemistry hero, Hiroki Sayama tweeting a link to How a life-like system emerges from a simple particle motion law, I thought I'd dust off Houdini to see if I could implement this model in VEX. The paper discusses a simple particle system, named Primordial Particle Systems (PPS), that leads to life-like structures through morphogenesis. Each particle in the system is defined by its position and heading and, with each step in the simulation, alters its heading based on the PPS rule and moves forward at a defined speed. The heading is updated based on the number of neighbors to the particle's left and right. The project set up is super simple:
Inside a geometry node, I create a grid, and randomly scatter 19,000 points across it. An attribute wrangle node assigns a random value to @angle:
@angle = $PI * 2 * rand(@ptnum);
The real magic happens inside another attribute wrangle inside the solver. In a nutshell, my VEX code iterates over each point's neighbors and sums the neighbor count to its left and right. To figure out the chirality, I use some simple trigonometry to rotate the vector defined by the current particle and the neighbor by the current particle's angle, then calculate the angle of the rotated vector.
Not quite finally, because to make things pretty, I update the color using the number of neighbors to control hue:
@Cd = hsvtorgb(N / maxParticles, 1.0, 1.0);
Easy! Solitons Emerging from Tweaked Model
I couldn't help tinkering with the published PPS math by making the speed a function of the number of local neighbors:
@speed = 1.5 * (N / maxParticles);
In the video above, alpha is 182° and beta is -13°. References Schmickl, T. et al. How a life-like system emerges from a simple particle motion law. Sci. Rep.6, 37969; doi: 10.1038/srep37969 (2016).
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